- Email: [email protected]
Microperforated insertion units: An alternative strategy to design microperforated panels
Applied Acoustics 67 (2006) 62–73 www.elsevier.com/locate/apacoust
Technical note
Microperforated insertion units: An alternative strategy to design microperforated panels Jaime Pfretzschner *, Pedro Cobo, Francisco Simo´n, Marı´a Cuesta, Alejandro Ferna´ndez Instituto de Acu´stica, CSIC, Serrano 144, 28006 Madrid, Spain Received 15 October 2004; received in revised form 15 April 2005; accepted 4 May 2005 Available online 28 June 2005
Abstract Microperforated panels (MPPs) coupled to a rigid wall have been proposed recently as an alternative to porous absorbers in situations having concerns with bacterial contamination and small particles discharge, like food, pharmaceutical and microelectronic industries. There exists also an increasing interest for MPP absorbers in the transportation industry and civil engineering. In general, an optimally designed MPP with good broadband absorption requires many submillimetric holes distributed over a panel of also submillimetric thickness. Such thin plates or foils become so fragile that they need to be protected from mechanical damage. In this paper, an alternative strategy is investigated which allows the design of MPPs with panels of millimetric thickness while maintaining their acoustic performance. These absorbers, named microperforated insertion units (MIUs), avoid the structural problems of the classical MPPs. An assessment of the sound absorption properties of these structures is presented. Comparisons between calculations and measurements are also made under two experimental conditions: plane waves at normal incidence (impedance tube) and free field (anechoic room). 2005 Elsevier Ltd. All rights reserved. Keywords: Sound absorption; Microperforated panels; Microperforated insertion units
*
Corresponding author. Tel.: +34 915618806; fax: +34 914117651. E-mail address: [email protected] (J. Pfretzschner).
0003-682X/$ - see front matter 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.apacoust.2005.05.005
J. Pfretzschner et al. / Applied Acoustics 67 (2006) 62–73
63
1. Introduction The fundamentals of MPPs as sound absorbers were developed in the late sixties by Maa [1] for its use in those situations where the traditional fibrous absorbers are discarded due to health or cleaning reasons. A MPP consists of a sheet panel with small perforations distributed over its surface. When these perforations are of submillimetric size (diameter 0.5–1 mm) they provide by themselves enough acoustic resistance and low acoustic mass reactance necessary for a wideband absorber (one or two octaves). The MPPs are tuned type absorbers, requiring an air space between the perforated panel and the backing wall in which they are installed. MPPs have been developed for a number of years, and the theoretical principles and algorithms which describe its acoustic properties are well known [1–6]. Whilst the original Maa model considered a rigid plate coupled to a hard wall through an air cavity, other authors have extended it to take into account both the plate vibrations [7] and a flexible wall [8]. The absorption spectrum can be broadened by adding a second MPP in series with the primary one [1,7,9]. MPPs have been used as transparent acrylglass panels for the improvement of the acoustics in the German Bundestag in Bonn [10], or as transparent foils in order to improve the insertion loss of windows [11]. Wu [12] described the advantages of using MPPs instead of porous materials as sound absorbers in silencers, since they lack of problems such as bacterial pollution (hospitals, food industries,. . .) and small particle discharge (white chambers in micro-electronics). Some other applications of MPPs have been described recently. For instance, double panels with MPPs have been proposed to increase the sound transmission loss at low frequencies, replacing the traditional technologies [13,14]. The MPP acts as an acoustical damping material to reduce the structure-borne sound radiation from a double-leaf structure, avoiding the amplification effect due to the mass– air–mass resonance. An interesting application of the same strategy can be found in aircraft acoustics, where high sound transmission loss is demanded compatible with low weight [15]. Recently, MPPs have been used in combination with active control to implement hybrid passive–active systems which provide wideband absorption including low frequencies [16–18]. The overall thickness of a hybrid system can be significantly decreased by using MPPs. According to Maa [3], the diameter hole-to-panel thickness ratio should be nearly one to obtain a MPP with optimal absorption properties. Therefore, such rather thin panels (with submillimetric thickness) could produce structural troubles related to their installation as sound absorbers. This paper presents an alternative strategy to develop more structurally robust MPPs. The first idea was to design some kind of hollow pieces, Fig. 1, covered by a thin wire mesh microperforated insertion units (MIU) that can be inserted in a reflecting wall or panel in order to convert it to absorptive [19]. This paper considers the simplest case consisting in a rigid perforated panel, with low acoustic resistance, whose perforations are covered (hard contact) with a specific wire mesh, raising in this way the total acoustic resistance of the structure.
64
J. Pfretzschner et al. / Applied Acoustics 67 (2006) 62–73
Fig. 1. Several mechanical solutions to implement a MIU.
Section 2 describes the fundamentals of MIUs. In Section 3, some experimental results which validate the proposed design are reported.
2. Microperforated insertion units (MIUs) The MPP described in the literature has absorption curves with one or two octave bands, corresponding to pore diameters of about 0.5 mm, and percentages of open area of the order of 3%. To increase the bandwidth of the absorption curves (maintaining constant the open area ratio) it is necessary to diminish the diameter of the pores and, in consequence, to increase the number of them in progressively thinner foils. Fig. 2 shows the absorption coefficient of a MPP as a function of the frequency (100 < f < 4000 Hz) and the diameter of the perforations (35 lm < d < 1 mm), with an open area fraction p = 1% and an air cavity D = 0.1 m. Horizontal intersections should provide the absorption curves for a given perforation diameter. It can be seen that a good compromise between high values of the maxima and broadband absorption can be obtained with d < 100 lm. In comparison, similar curves of absorption can be found for a layer of mineral wool with flow resistivity 47,000 rayl/m, thickness 1.5 cm, and air cavity 8.5 cm, and also for a sheet of resistive woven metal or non-woven glass materials with flow resistance, normalised to the air characteristic acoustic impedance, of 1.7, and air cavity of 10 cm. The above examples provide absorbers with frequency bands wider than three octaves. A MPP with absorption performance similar to that sheet must have very small perforation diameter (and as a consequence reduced plate thickness) and increased
J. Pfretzschner et al. / Applied Acoustics 67 (2006) 62–73
65
Fig. 2. Absorption coefficient of an MPP as a function of the frequency, f, and perforation diameter, d, keeping constant the other three parameters (d = t, p = 1%, D = 10 cm).
number of perforations in order to maintain the open area fraction. The drill must be thinner (more fragile) or other mechanical perforation system should be used (for instance, laser technology). Furthermore, to optimize the absorption performance of the MPP, a noticeable reduction of the plate thickness should be made (d t). As a consequence, the MPP becomes so delicate and fragile that it should be managed carefully and that, in turn, will discourage its use outdoors. Thus, a MPP appropriate for use as a practical sound absorber should have the following characteristics: Perforations with small diameters (in order to increase the frequency band of the absorption coefficient). Small perforation coefficient (<10% for aesthetic reasons). Mechanical stability and manageability (plates with thickness wider than 1 mm). Cheap and easy to install. Easy to clean and resistant to cleaning processes. These requirements seem to conflict each other. A procedure to implement MPPs is proposed which solve this conflict. Let start with a double MPP similar to that proposed by Maa to widen the absorption band [1], Fig. 3(a). The classical Maa double MPP resonator has a first panel with parameters (d1, t1, p1, D1) and a second panel with parameters (d2, t2, p2, D2). The proposal is to combine the parameters (d1, t1, p1)
66
J. Pfretzschner et al. / Applied Acoustics 67 (2006) 62–73
Fig. 3. Double layer structure (a) and equivalent electrical circuit (b) of a double MPP.
of the first MPP and (d2, t2, p2) of the second MPP (a micrometric wire mesh for instance) in such a way that, when the first air cavity thickness, D1, is reduced to zero, an unique MPP is obtained with the desired performance, Fig. 3(b). The combination of the perforated plate with the wire mesh in ‘‘hard’’ contact allows increasing the average resistance of the unit, so that the flow velocity through a hole of the wire mesh is the same as the flow velocity in a hole of the carrying plate [6]. In this way, the cross-sectional average particle velocity (or volume velocity of the flow per unit cross-sectional area) equals the average particle velocity within the channels multiplied by the open area fraction [5]. As a result, the impedance of the combination will be the addition of the acoustic impedance of the perforated plate plus the impedance of the wire mesh divided by the open area fraction of the plate. The absorber obtained by this procedure [19], named microperforated insertion unit (MIU), can be designed with a first thicker, less perforated, larger holes panel followed by a second thinner, more perforated, and smaller holes panel. Fig. 4 compares the absorption curves of a single MPP with parameters (d, t, p, D) = (0.3 mm, 0.4 mm, 1.7%, 5 cm), a double MPP with parameters (d1, t1, p1, D1, d2, t2, p2, D2) = (0.3 mm,0.4 mm,1.7%, 5 cm, 0.3 mm, 0.4 mm, 1.7%, 10 cm), and a MIU with parameters (d1, t1, p1, d2, t2, p2, D2) = (6 mm, 3 mm, 14%, 39 lm, 35 lm, 1.96%, 8 cm). The MIU has the additional advantage that requires a thinner air cavity that those of the classical double MPPs. In the case reported in Fig. 4 the whole thickness of the MIU is 8 cm instead of the 15 cm required for the double MPP. Standard metal, plastic, or even cardboard panels could be combined with commercial micrometric meshes (or non-woven glass or open weave textiles with appropriate acoustic resistances). The absorption coefficient of the MIU will depend on seven parameters (t1, d1, p1, t2, d2, p2, D2). However, since the second MPP is chosen from commercial meshes, the three parameters (d2, t2, p2) are usually fixed. Thus, a graphical analysis of the dependence of the MIU with the following parameters has been made: The thickness of the carrying plate (t1). The number of perforations and their diameters, d1, such that the perforation coefficient of the plate (p1) is kept constant.
J. Pfretzschner et al. / Applied Acoustics 67 (2006) 62–73
67
Fig. 4. Absorption of three probes: (dotted line) single MPP, (d, t, p, D) = (0.3 mm, 0.4 mm, 1.7%, 5 cm); (dashed line) double MPP, (d1, t1, p1, D1, d2, t2, p2, D2) = (0.3 mm, 0.4 mm, 1.7%, 5 cm, 0.3 mm, 0.4 mm, 1.7%, 10 cm); (solid line) MIU, (d1, t1, p1, D1, d2, t2, p2, D2) = (6 mm, 3 mm, 14%, 0 cm, 39 lm, 35 lm, 1.96%, 8 cm).
Fig. 5. Absorption curves of a MIU: d1 = 6 mm, p1 = 10%, t2 = 35 lm, d2 = 39 lm, p2 = 1.4%, D2 = 20, and t1 = 1 mm (solid line), 4 mm (dotted line), 8 mm (dashed line), and 12 mm (dashed-dotted line).
68
J. Pfretzschner et al. / Applied Acoustics 67 (2006) 62–73
Fig. 5 shows the absorption curves of the resulting MIU when a commercial mesh of d2 = 39 lm, t2 = 35 lm, and p2 = 1.4% (measured with an optical microscope), is combined with a carrying panel of d1 = 6 mm, p1 = 10%, and t1 varying from 1 mm to 12 mm. When the panel thickness increases the absorption lobes of the MIU shift towards lower frequencies and become narrower. Nevertheless, the absorption curves remain very similar for thicknesses ranging from 0.5 to 8 mm. The perforation ratio of the plate is obtained from the number of the individual holes and their diameters. Maintaining the perforation ratio p1 constant, larger diameters d1 require a lower number of holes. Fig. 6 illustrates the dependence of the absorption coefficient of the MIU with the number and diameter of the holes keeping constant the perforation ratio, p1 = 10%. In this case, this perforation ratio is provided by either 28 holes with d1 = 6 mm, 16 holes with d1 = 7.9 m, 4 holes with d1 = 15.8 mm, or 1 hole with d1 = 31.6 mm. As it can be seen, the absorption lobes move towards lower frequencies becoming narrower when the hole diameter increases and the number of holes decreases. 3. Experimental results In order to validate the procedure described above for MIU designing, a MIU was devised to absorb low frequencies in more than three octaves. This MIU was made using a 1 mm thick panel with 8 holes with diameter 12 mm (p1 = 11.5%) covered with a micrometric mesh with measured parameters (d2, t2, p2) = (39 lm,
Fig. 6. Absorption curves of a MIU with t1 = 1 mm, p1 = 10%, t2 = 35 lm, d2 = 39 lm, p2 = 1.4%, D2 = 20 cm, and d1 = 6 mm (solid line), 7.9 mm (dotted line), 15.8 mm (dashed line), or 31.6 mm (dasheddotted line). The number of holes with diameter d1 is 28, 16, 4, and 1, respectively.
J. Pfretzschner et al. / Applied Acoustics 67 (2006) 62–73
69
35 lm, 1.4%), leaving an air cavity of D2 = 20 cm between the MIU and the back wall. Fig. 7 shows superimposed the predicted and the measured absorption curves. For the measurement, a two-microphone impedance tube (B & K Type 4206), with diameter 10 cm, fed with random noise was used. Due to the limitations of the
Fig. 7. Above: view of the MIU (t1, d1, p1, t2, d2, p2, D2) = (1 mm, 12 mm, 11.5%, 35 lm, 39 lm, 1.54%, 20 cm). Below: theoretical (solid) and measured (dashed) absorption curves.
70
J. Pfretzschner et al. / Applied Acoustics 67 (2006) 62–73
system, the experimental curve contains frequencies just up to 1600 Hz. Reasonable agreement is obtained between the predicted and measured curves. To illustrate the behaviour of the MIU at higher frequencies, other results are presented in Fig. 8. In this case, the 3 cm diameter impedance tube was used for the measurement, so that the reliable higher frequency goes up to 6400 Hz. This MIU
Fig. 8. Above: view of the MIU (t1, d1, p1, t2, d2, p2, D2) = (1 mm, 5.5 mm, 10.1%, 35 lm, 39 lm, 1.4%, 20 cm). Below: theoretical (solid) and measured (dashed) absorption curves.
J. Pfretzschner et al. / Applied Acoustics 67 (2006) 62–73
71
Fig. 9. Above: view of a 2.44 · 2.44 m2 large MIU (t1, d1, p1, t2, d2, p2, D2) = (1 mm, 8 mm, 9.9%, 35 lm, 39 lm, 1.4%, 5 cm). Below: theoretical (solid) and measured (dashed) absorption curves.
72
J. Pfretzschner et al. / Applied Acoustics 67 (2006) 62–73
consists of a 1 mm thick plate with three holes of 5.5 mm diameter (p1 = 10.1%), covered with the same wire mesh than the previous test probe and the same air space D2 = 20 cm. It can be seen the good agreement between experimental and calculated curves. As a third example, Fig. 9 shows the calculated and experimental curves of a large perforated panel of size (2.44 · 2.44 m2), with similar characteristics as the one from the described in Fig. 7 (same wire mesh, 10% open area fraction, and 1 mm panel thickness, but only 5 cm back cavity). In this case the experimental curves have been measured in an anechoic room using MLS signals with the subtraction technique [20]. To avoid diffractions in the panel edges, the reflected signal has been windowed, this setting a reliable lower frequency of 240 Hz. Again there exists a good concordance between experimental and calculated results. 4. Conclusions An alternative design procedure of MPPs absorbers is proposed with the introduction of the MIU technology. It allows a practical design of almost any broadband acoustic absorber in a quick and simple way. A MIU can be obtained by combining two perforated panels with appropriate constitutive parameters. Each one operating individually does not provide good absorption performance. One of them is too thick with too large perforations. The other is too thin and has a very high perforation ratio. However their combination can produce absorption over two or three octave bands. Since the resulting MIU has the thickness of the first plate, it lacks of the mechanical constraints of the equivalent MPP. A great number of applications can be envisaged, both in room acoustics and industrial noise control. Leaving an air cavity behind, this design enables to convert any reflecting surface into absorptive. Acknowledgements We are grateful to the Spanish Ministry of Science and Technology for funding this research under Grants No. DPI2001-1613-C02-01 and DPI2004-05504-C02-01.
References [1] [2] [3] [4]
Maa DY. Microperforated – panel wideband absorbers. Noise Control Eng J 1985;29(3):77–87. Crandall JB. Theory of vibrating systems and sound. New York: Van Nostrand; 1926. Maa DY. Potential of microperforated panel absorber. J Acoust Soc Am 1988;104(5):2861–6. Cremer L, Mu¨ller H. Principles and applications of room acoustics, vol. 2. Applied Science Publishers Ltd; 1982. [5] Fahy F. Foundations of engineering acoustics. New York: Academic Press; 2001. [6] Ingard U. Notes on sound absorption. Maine: KitteryPoint; 1999. [7] Kang J, Fuchs HV. Predicting the absorption of open weave textiles and micro-perforated membranes backed by an air space. J Sound Vib 1999;220(5):905–20.
J. Pfretzschner et al. / Applied Acoustics 67 (2006) 62–73
73
[8] Dupont T, Pavic G, Laulagnet B. Acoustic properties of lightweight micro-perforated plate systems. Acta Acust 2003;89(2):201–12. [9] Fuchs HV, Zha X. Einsatz mikro – perforierter Platten als Schallabsorber mit inha¨renter Da¨mpfung. Acustica 1995;81(2):107–16. [10] Fuchs HV, Zha X. Acrylic-glass sound absorbers in the plenum of the Deutscher Bundestag. Appl Acoust 1997;51(2):211–7. [11] Kang J, Brocklesby MW. Feasibility of applying micro – perforated absorbers in acoustic window systems. Appl Acoust 2005;66:669–89. [12] Wu MQ. Micro-perforated panels for duct silencing. Noise Control Eng 1997;45(2):69–77. [13] Thomas C, Weltin U, Petersen S. Sound transmission loss of double – panel partitions with internal microperforated panel absorbers. In: Proceedings of the 10th international congress on sound and vibration; 2003. p. 4649–56. [14] Yairi M, Sakagami K, Morimoto M, Minemura A, Andow K. Effect of a microperforated panel inside the cavity on structure borne sound radiation from a double-leaf structure. In: Proceedings of the ICA; 2004. p. II.1399–II.1402. [15] Thomas C, Weltin U. Sound reduction of double walls containing inner microperforated panel absorbers. In: Proceedings of the ICA; 2004. p. II.1403–II.1406. [16] Pfretzschner J, Cobo P, Bote D, Fernandez A, Doutres O. Active control and microperforated panels. In: Proceedings of the Euronoise (Naples); 2003. p. ID 144. [17] Cobo P, Pfretzschner J, Cuesta M, Fernandez A. Hybrid passive-active sound absorption in a standing wave tube using a thin plate actuator as secondary source. In Proceedings of the ICA; 2004. p. II.1281–II.1284. [18] Cobo P, Pfretzschner J, Cuesta M, Anthony DK. Hybrid passive-active -absorption using microperforated panels. J Acoust Soc Am 2004;112(3):2118–25. [19] Pfretzschner J, Cobo P, Simon F. Using microperforated insertion units as sound absorbers. Patent pending; 2004 [in Spanish]. [20] Mommertz E. Angle-dependent in situ measurements of reflection coefficients using a subtraction technique. Appl Acoust 1995;46:251–63.
Technical note
Microperforated insertion units: An alternative strategy to design microperforated panels Jaime Pfretzschner *, Pedro Cobo, Francisco Simo´n, Marı´a Cuesta, Alejandro Ferna´ndez Instituto de Acu´stica, CSIC, Serrano 144, 28006 Madrid, Spain Received 15 October 2004; received in revised form 15 April 2005; accepted 4 May 2005 Available online 28 June 2005
Abstract Microperforated panels (MPPs) coupled to a rigid wall have been proposed recently as an alternative to porous absorbers in situations having concerns with bacterial contamination and small particles discharge, like food, pharmaceutical and microelectronic industries. There exists also an increasing interest for MPP absorbers in the transportation industry and civil engineering. In general, an optimally designed MPP with good broadband absorption requires many submillimetric holes distributed over a panel of also submillimetric thickness. Such thin plates or foils become so fragile that they need to be protected from mechanical damage. In this paper, an alternative strategy is investigated which allows the design of MPPs with panels of millimetric thickness while maintaining their acoustic performance. These absorbers, named microperforated insertion units (MIUs), avoid the structural problems of the classical MPPs. An assessment of the sound absorption properties of these structures is presented. Comparisons between calculations and measurements are also made under two experimental conditions: plane waves at normal incidence (impedance tube) and free field (anechoic room). 2005 Elsevier Ltd. All rights reserved. Keywords: Sound absorption; Microperforated panels; Microperforated insertion units
*
Corresponding author. Tel.: +34 915618806; fax: +34 914117651. E-mail address: [email protected] (J. Pfretzschner).
0003-682X/$ - see front matter 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.apacoust.2005.05.005
J. Pfretzschner et al. / Applied Acoustics 67 (2006) 62–73
63
1. Introduction The fundamentals of MPPs as sound absorbers were developed in the late sixties by Maa [1] for its use in those situations where the traditional fibrous absorbers are discarded due to health or cleaning reasons. A MPP consists of a sheet panel with small perforations distributed over its surface. When these perforations are of submillimetric size (diameter 0.5–1 mm) they provide by themselves enough acoustic resistance and low acoustic mass reactance necessary for a wideband absorber (one or two octaves). The MPPs are tuned type absorbers, requiring an air space between the perforated panel and the backing wall in which they are installed. MPPs have been developed for a number of years, and the theoretical principles and algorithms which describe its acoustic properties are well known [1–6]. Whilst the original Maa model considered a rigid plate coupled to a hard wall through an air cavity, other authors have extended it to take into account both the plate vibrations [7] and a flexible wall [8]. The absorption spectrum can be broadened by adding a second MPP in series with the primary one [1,7,9]. MPPs have been used as transparent acrylglass panels for the improvement of the acoustics in the German Bundestag in Bonn [10], or as transparent foils in order to improve the insertion loss of windows [11]. Wu [12] described the advantages of using MPPs instead of porous materials as sound absorbers in silencers, since they lack of problems such as bacterial pollution (hospitals, food industries,. . .) and small particle discharge (white chambers in micro-electronics). Some other applications of MPPs have been described recently. For instance, double panels with MPPs have been proposed to increase the sound transmission loss at low frequencies, replacing the traditional technologies [13,14]. The MPP acts as an acoustical damping material to reduce the structure-borne sound radiation from a double-leaf structure, avoiding the amplification effect due to the mass– air–mass resonance. An interesting application of the same strategy can be found in aircraft acoustics, where high sound transmission loss is demanded compatible with low weight [15]. Recently, MPPs have been used in combination with active control to implement hybrid passive–active systems which provide wideband absorption including low frequencies [16–18]. The overall thickness of a hybrid system can be significantly decreased by using MPPs. According to Maa [3], the diameter hole-to-panel thickness ratio should be nearly one to obtain a MPP with optimal absorption properties. Therefore, such rather thin panels (with submillimetric thickness) could produce structural troubles related to their installation as sound absorbers. This paper presents an alternative strategy to develop more structurally robust MPPs. The first idea was to design some kind of hollow pieces, Fig. 1, covered by a thin wire mesh microperforated insertion units (MIU) that can be inserted in a reflecting wall or panel in order to convert it to absorptive [19]. This paper considers the simplest case consisting in a rigid perforated panel, with low acoustic resistance, whose perforations are covered (hard contact) with a specific wire mesh, raising in this way the total acoustic resistance of the structure.
64
J. Pfretzschner et al. / Applied Acoustics 67 (2006) 62–73
Fig. 1. Several mechanical solutions to implement a MIU.
Section 2 describes the fundamentals of MIUs. In Section 3, some experimental results which validate the proposed design are reported.
2. Microperforated insertion units (MIUs) The MPP described in the literature has absorption curves with one or two octave bands, corresponding to pore diameters of about 0.5 mm, and percentages of open area of the order of 3%. To increase the bandwidth of the absorption curves (maintaining constant the open area ratio) it is necessary to diminish the diameter of the pores and, in consequence, to increase the number of them in progressively thinner foils. Fig. 2 shows the absorption coefficient of a MPP as a function of the frequency (100 < f < 4000 Hz) and the diameter of the perforations (35 lm < d < 1 mm), with an open area fraction p = 1% and an air cavity D = 0.1 m. Horizontal intersections should provide the absorption curves for a given perforation diameter. It can be seen that a good compromise between high values of the maxima and broadband absorption can be obtained with d < 100 lm. In comparison, similar curves of absorption can be found for a layer of mineral wool with flow resistivity 47,000 rayl/m, thickness 1.5 cm, and air cavity 8.5 cm, and also for a sheet of resistive woven metal or non-woven glass materials with flow resistance, normalised to the air characteristic acoustic impedance, of 1.7, and air cavity of 10 cm. The above examples provide absorbers with frequency bands wider than three octaves. A MPP with absorption performance similar to that sheet must have very small perforation diameter (and as a consequence reduced plate thickness) and increased
J. Pfretzschner et al. / Applied Acoustics 67 (2006) 62–73
65
Fig. 2. Absorption coefficient of an MPP as a function of the frequency, f, and perforation diameter, d, keeping constant the other three parameters (d = t, p = 1%, D = 10 cm).
number of perforations in order to maintain the open area fraction. The drill must be thinner (more fragile) or other mechanical perforation system should be used (for instance, laser technology). Furthermore, to optimize the absorption performance of the MPP, a noticeable reduction of the plate thickness should be made (d t). As a consequence, the MPP becomes so delicate and fragile that it should be managed carefully and that, in turn, will discourage its use outdoors. Thus, a MPP appropriate for use as a practical sound absorber should have the following characteristics: Perforations with small diameters (in order to increase the frequency band of the absorption coefficient). Small perforation coefficient (<10% for aesthetic reasons). Mechanical stability and manageability (plates with thickness wider than 1 mm). Cheap and easy to install. Easy to clean and resistant to cleaning processes. These requirements seem to conflict each other. A procedure to implement MPPs is proposed which solve this conflict. Let start with a double MPP similar to that proposed by Maa to widen the absorption band [1], Fig. 3(a). The classical Maa double MPP resonator has a first panel with parameters (d1, t1, p1, D1) and a second panel with parameters (d2, t2, p2, D2). The proposal is to combine the parameters (d1, t1, p1)
66
J. Pfretzschner et al. / Applied Acoustics 67 (2006) 62–73
Fig. 3. Double layer structure (a) and equivalent electrical circuit (b) of a double MPP.
of the first MPP and (d2, t2, p2) of the second MPP (a micrometric wire mesh for instance) in such a way that, when the first air cavity thickness, D1, is reduced to zero, an unique MPP is obtained with the desired performance, Fig. 3(b). The combination of the perforated plate with the wire mesh in ‘‘hard’’ contact allows increasing the average resistance of the unit, so that the flow velocity through a hole of the wire mesh is the same as the flow velocity in a hole of the carrying plate [6]. In this way, the cross-sectional average particle velocity (or volume velocity of the flow per unit cross-sectional area) equals the average particle velocity within the channels multiplied by the open area fraction [5]. As a result, the impedance of the combination will be the addition of the acoustic impedance of the perforated plate plus the impedance of the wire mesh divided by the open area fraction of the plate. The absorber obtained by this procedure [19], named microperforated insertion unit (MIU), can be designed with a first thicker, less perforated, larger holes panel followed by a second thinner, more perforated, and smaller holes panel. Fig. 4 compares the absorption curves of a single MPP with parameters (d, t, p, D) = (0.3 mm, 0.4 mm, 1.7%, 5 cm), a double MPP with parameters (d1, t1, p1, D1, d2, t2, p2, D2) = (0.3 mm,0.4 mm,1.7%, 5 cm, 0.3 mm, 0.4 mm, 1.7%, 10 cm), and a MIU with parameters (d1, t1, p1, d2, t2, p2, D2) = (6 mm, 3 mm, 14%, 39 lm, 35 lm, 1.96%, 8 cm). The MIU has the additional advantage that requires a thinner air cavity that those of the classical double MPPs. In the case reported in Fig. 4 the whole thickness of the MIU is 8 cm instead of the 15 cm required for the double MPP. Standard metal, plastic, or even cardboard panels could be combined with commercial micrometric meshes (or non-woven glass or open weave textiles with appropriate acoustic resistances). The absorption coefficient of the MIU will depend on seven parameters (t1, d1, p1, t2, d2, p2, D2). However, since the second MPP is chosen from commercial meshes, the three parameters (d2, t2, p2) are usually fixed. Thus, a graphical analysis of the dependence of the MIU with the following parameters has been made: The thickness of the carrying plate (t1). The number of perforations and their diameters, d1, such that the perforation coefficient of the plate (p1) is kept constant.
J. Pfretzschner et al. / Applied Acoustics 67 (2006) 62–73
67
Fig. 4. Absorption of three probes: (dotted line) single MPP, (d, t, p, D) = (0.3 mm, 0.4 mm, 1.7%, 5 cm); (dashed line) double MPP, (d1, t1, p1, D1, d2, t2, p2, D2) = (0.3 mm, 0.4 mm, 1.7%, 5 cm, 0.3 mm, 0.4 mm, 1.7%, 10 cm); (solid line) MIU, (d1, t1, p1, D1, d2, t2, p2, D2) = (6 mm, 3 mm, 14%, 0 cm, 39 lm, 35 lm, 1.96%, 8 cm).
Fig. 5. Absorption curves of a MIU: d1 = 6 mm, p1 = 10%, t2 = 35 lm, d2 = 39 lm, p2 = 1.4%, D2 = 20, and t1 = 1 mm (solid line), 4 mm (dotted line), 8 mm (dashed line), and 12 mm (dashed-dotted line).
68
J. Pfretzschner et al. / Applied Acoustics 67 (2006) 62–73
Fig. 5 shows the absorption curves of the resulting MIU when a commercial mesh of d2 = 39 lm, t2 = 35 lm, and p2 = 1.4% (measured with an optical microscope), is combined with a carrying panel of d1 = 6 mm, p1 = 10%, and t1 varying from 1 mm to 12 mm. When the panel thickness increases the absorption lobes of the MIU shift towards lower frequencies and become narrower. Nevertheless, the absorption curves remain very similar for thicknesses ranging from 0.5 to 8 mm. The perforation ratio of the plate is obtained from the number of the individual holes and their diameters. Maintaining the perforation ratio p1 constant, larger diameters d1 require a lower number of holes. Fig. 6 illustrates the dependence of the absorption coefficient of the MIU with the number and diameter of the holes keeping constant the perforation ratio, p1 = 10%. In this case, this perforation ratio is provided by either 28 holes with d1 = 6 mm, 16 holes with d1 = 7.9 m, 4 holes with d1 = 15.8 mm, or 1 hole with d1 = 31.6 mm. As it can be seen, the absorption lobes move towards lower frequencies becoming narrower when the hole diameter increases and the number of holes decreases. 3. Experimental results In order to validate the procedure described above for MIU designing, a MIU was devised to absorb low frequencies in more than three octaves. This MIU was made using a 1 mm thick panel with 8 holes with diameter 12 mm (p1 = 11.5%) covered with a micrometric mesh with measured parameters (d2, t2, p2) = (39 lm,
Fig. 6. Absorption curves of a MIU with t1 = 1 mm, p1 = 10%, t2 = 35 lm, d2 = 39 lm, p2 = 1.4%, D2 = 20 cm, and d1 = 6 mm (solid line), 7.9 mm (dotted line), 15.8 mm (dashed line), or 31.6 mm (dasheddotted line). The number of holes with diameter d1 is 28, 16, 4, and 1, respectively.
J. Pfretzschner et al. / Applied Acoustics 67 (2006) 62–73
69
35 lm, 1.4%), leaving an air cavity of D2 = 20 cm between the MIU and the back wall. Fig. 7 shows superimposed the predicted and the measured absorption curves. For the measurement, a two-microphone impedance tube (B & K Type 4206), with diameter 10 cm, fed with random noise was used. Due to the limitations of the
Fig. 7. Above: view of the MIU (t1, d1, p1, t2, d2, p2, D2) = (1 mm, 12 mm, 11.5%, 35 lm, 39 lm, 1.54%, 20 cm). Below: theoretical (solid) and measured (dashed) absorption curves.
70
J. Pfretzschner et al. / Applied Acoustics 67 (2006) 62–73
system, the experimental curve contains frequencies just up to 1600 Hz. Reasonable agreement is obtained between the predicted and measured curves. To illustrate the behaviour of the MIU at higher frequencies, other results are presented in Fig. 8. In this case, the 3 cm diameter impedance tube was used for the measurement, so that the reliable higher frequency goes up to 6400 Hz. This MIU
Fig. 8. Above: view of the MIU (t1, d1, p1, t2, d2, p2, D2) = (1 mm, 5.5 mm, 10.1%, 35 lm, 39 lm, 1.4%, 20 cm). Below: theoretical (solid) and measured (dashed) absorption curves.
J. Pfretzschner et al. / Applied Acoustics 67 (2006) 62–73
71
Fig. 9. Above: view of a 2.44 · 2.44 m2 large MIU (t1, d1, p1, t2, d2, p2, D2) = (1 mm, 8 mm, 9.9%, 35 lm, 39 lm, 1.4%, 5 cm). Below: theoretical (solid) and measured (dashed) absorption curves.
72
J. Pfretzschner et al. / Applied Acoustics 67 (2006) 62–73
consists of a 1 mm thick plate with three holes of 5.5 mm diameter (p1 = 10.1%), covered with the same wire mesh than the previous test probe and the same air space D2 = 20 cm. It can be seen the good agreement between experimental and calculated curves. As a third example, Fig. 9 shows the calculated and experimental curves of a large perforated panel of size (2.44 · 2.44 m2), with similar characteristics as the one from the described in Fig. 7 (same wire mesh, 10% open area fraction, and 1 mm panel thickness, but only 5 cm back cavity). In this case the experimental curves have been measured in an anechoic room using MLS signals with the subtraction technique [20]. To avoid diffractions in the panel edges, the reflected signal has been windowed, this setting a reliable lower frequency of 240 Hz. Again there exists a good concordance between experimental and calculated results. 4. Conclusions An alternative design procedure of MPPs absorbers is proposed with the introduction of the MIU technology. It allows a practical design of almost any broadband acoustic absorber in a quick and simple way. A MIU can be obtained by combining two perforated panels with appropriate constitutive parameters. Each one operating individually does not provide good absorption performance. One of them is too thick with too large perforations. The other is too thin and has a very high perforation ratio. However their combination can produce absorption over two or three octave bands. Since the resulting MIU has the thickness of the first plate, it lacks of the mechanical constraints of the equivalent MPP. A great number of applications can be envisaged, both in room acoustics and industrial noise control. Leaving an air cavity behind, this design enables to convert any reflecting surface into absorptive. Acknowledgements We are grateful to the Spanish Ministry of Science and Technology for funding this research under Grants No. DPI2001-1613-C02-01 and DPI2004-05504-C02-01.
References [1] [2] [3] [4]
Maa DY. Microperforated – panel wideband absorbers. Noise Control Eng J 1985;29(3):77–87. Crandall JB. Theory of vibrating systems and sound. New York: Van Nostrand; 1926. Maa DY. Potential of microperforated panel absorber. J Acoust Soc Am 1988;104(5):2861–6. Cremer L, Mu¨ller H. Principles and applications of room acoustics, vol. 2. Applied Science Publishers Ltd; 1982. [5] Fahy F. Foundations of engineering acoustics. New York: Academic Press; 2001. [6] Ingard U. Notes on sound absorption. Maine: KitteryPoint; 1999. [7] Kang J, Fuchs HV. Predicting the absorption of open weave textiles and micro-perforated membranes backed by an air space. J Sound Vib 1999;220(5):905–20.
J. Pfretzschner et al. / Applied Acoustics 67 (2006) 62–73
73
[8] Dupont T, Pavic G, Laulagnet B. Acoustic properties of lightweight micro-perforated plate systems. Acta Acust 2003;89(2):201–12. [9] Fuchs HV, Zha X. Einsatz mikro – perforierter Platten als Schallabsorber mit inha¨renter Da¨mpfung. Acustica 1995;81(2):107–16. [10] Fuchs HV, Zha X. Acrylic-glass sound absorbers in the plenum of the Deutscher Bundestag. Appl Acoust 1997;51(2):211–7. [11] Kang J, Brocklesby MW. Feasibility of applying micro – perforated absorbers in acoustic window systems. Appl Acoust 2005;66:669–89. [12] Wu MQ. Micro-perforated panels for duct silencing. Noise Control Eng 1997;45(2):69–77. [13] Thomas C, Weltin U, Petersen S. Sound transmission loss of double – panel partitions with internal microperforated panel absorbers. In: Proceedings of the 10th international congress on sound and vibration; 2003. p. 4649–56. [14] Yairi M, Sakagami K, Morimoto M, Minemura A, Andow K. Effect of a microperforated panel inside the cavity on structure borne sound radiation from a double-leaf structure. In: Proceedings of the ICA; 2004. p. II.1399–II.1402. [15] Thomas C, Weltin U. Sound reduction of double walls containing inner microperforated panel absorbers. In: Proceedings of the ICA; 2004. p. II.1403–II.1406. [16] Pfretzschner J, Cobo P, Bote D, Fernandez A, Doutres O. Active control and microperforated panels. In: Proceedings of the Euronoise (Naples); 2003. p. ID 144. [17] Cobo P, Pfretzschner J, Cuesta M, Fernandez A. Hybrid passive-active sound absorption in a standing wave tube using a thin plate actuator as secondary source. In Proceedings of the ICA; 2004. p. II.1281–II.1284. [18] Cobo P, Pfretzschner J, Cuesta M, Anthony DK. Hybrid passive-active -absorption using microperforated panels. J Acoust Soc Am 2004;112(3):2118–25. [19] Pfretzschner J, Cobo P, Simon F. Using microperforated insertion units as sound absorbers. Patent pending; 2004 [in Spanish]. [20] Mommertz E. Angle-dependent in situ measurements of reflection coefficients using a subtraction technique. Appl Acoust 1995;46:251–63.